EXAMPLE 1 Use the formula for area of a circle

Find the indicated measure.

a. Area

r = 2.5 cm

SOLUTION

Write formula for the area of a circle.

= π (2.5)2 Substitute 2.5 for r.

= 6.25π Simplify.

≈ 19.63 Use a calculator.

A = πr2

The area about 19.63 square centimeters.

ANSWER

EXAMPLE 1 Use the formula for area of a circle

Find the indicated measure.

A = 113.1 cm2

b. DiameterWrite formula for the area of a circle.

Substitute 113.1 for A.113.1 = πr2

= r2113.1π

Divide each side by π.

6 ≈ r Find the positive square root of each side.

The radius is about 6 centimeters, so the diameter is about 12 centimeters.

ANSWER

A = πr2

SOLUTION

EXAMPLE 2 Find areas of sectors

Find the areas of the sectors formed by UTV.

SOLUTION

STEP 1Find the measures of the minor and major arcs.

Because m UTV = 70°, mUV = 70° and mUSV = 360° – 70° = 290°.

EXAMPLE 2

STEP 2

Find the areas of the small and large sectors.

Area of small sector = πr2

mUV360°

Write formula for area of a sector.

= π 8270°

360°Substitute.

≈ 39.10 Use a calculator.

Find areas of sectors

EXAMPLE 2

= π 82290°

360°Substitute.

≈ 161.97 Use a calculator.

Find areas of sectors

The areas of the small and large sectors are about 39.10 square units and 161.97 square units, respectively.

ANSWER

Area of large sector = πr2 mUSV360°

Write formula for area of a sector.

GUIDED PRACTICE for Examples 1 and 2

1. Area of D

Use the diagram to find the indicated measure.

SOLUTION

A = πr2 Write formula for the area of a circle.

= π (14)2 Substitute 14 for r.

= 196π Simplify.

= 617.75 Use a calculator

The area of D is about 615.75 ft2.

GUIDED PRACTICE for Examples 1 and 2

2. Area of red sector

SOLUTION

STEP 1

Find the measures of major arcs.

Use the diagram to find the indicated measure.

Because m FDE = 120, mFE = 120 and mFGE = 360 – 120 = 140.

GUIDED PRACTICE for Examples 1 and 2

Write formula for area of a sector.

= π 142120360

Substitute.

= 205.25 Use a calculator.

Area of red sector = π r2

mFE360

The area of red sector is about 205.25 ft2.

ANSWER

STEP 2

Find the area of red sector.

GUIDED PRACTICE for Examples 1 and 2

3. Area of blue sector

SOLUTION

STEP 1

Find the measure of the blue arc.

Because m FDE = 120, MFE = 120 and mFGE = 360 – 120 = 240.

Use the diagram to find the indicated measure.

GUIDED PRACTICE for Examples 1 and 2

Area of blue sector = π r2

mFEG360

Write formula for area of a sector.

= π 142240360

Substitute.

= 410.50 ft2 Use a calculator.

Area of blue sector is about 410.50 ft2.

ANSWER

STEP 2

Find the area of blue sector.